Weak solutions for a non-Newtonian diffuse interface model with different densities

Helmut Abels; Dominic Breit

doi:10.1088/0951-7715/29/11/3426

Weak solutions for a non-Newtonian diffuse interface model with different densities

Helmut Abels, Dominic Breit

Research output: Contribution to journal › Article › peer-review

18 Citations (Scopus)

Abstract

We consider weak solutions for a diffuse interface model of two non- Newtonian viscous, incompressible fluids of power-law type in the case of different densities in a bounded, sufficiently smooth domain. This leads to a coupled system of a nonhomogenouos generalized Navier-Stokes system and a Cahn-Hilliard equation. For the Cahn-Hilliard part a smooth free energy density and a constant, positive mobility is assumed. Using the L^∞-truncation method we prove existence of weak solutions for a power-law exponent p > 2d+2/d+2,d= 2, 3.

Original language	English
Pages (from-to)	3426-3453
Number of pages	28
Journal	Nonlinearity
Volume	29
Issue number	11
Early online date	19 Sept 2016
DOIs	https://doi.org/10.1088/0951-7715/29/11/3426
Publication status	Published - Nov 2016

Keywords

Cahn-Hilliard equation
diffuse interface model
L-truncation
non-Newtonian fluids
two-phase flow

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy
Applied Mathematics

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10.1088/0951-7715/29/11/3426

https://arxiv.org/abs/1509.05663v2

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abstract = "We consider weak solutions for a diffuse interface model of two non- Newtonian viscous, incompressible fluids of power-law type in the case of different densities in a bounded, sufficiently smooth domain. This leads to a coupled system of a nonhomogenouos generalized Navier-Stokes system and a Cahn-Hilliard equation. For the Cahn-Hilliard part a smooth free energy density and a constant, positive mobility is assumed. Using the L∞-truncation method we prove existence of weak solutions for a power-law exponent p > 2d+2/d+2,d= 2, 3.",

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AU - Abels, Helmut

AU - Breit, Dominic

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AB - We consider weak solutions for a diffuse interface model of two non- Newtonian viscous, incompressible fluids of power-law type in the case of different densities in a bounded, sufficiently smooth domain. This leads to a coupled system of a nonhomogenouos generalized Navier-Stokes system and a Cahn-Hilliard equation. For the Cahn-Hilliard part a smooth free energy density and a constant, positive mobility is assumed. Using the L∞-truncation method we prove existence of weak solutions for a power-law exponent p > 2d+2/d+2,d= 2, 3.

KW - Cahn-Hilliard equation

KW - diffuse interface model

KW - L-truncation

KW - non-Newtonian fluids

KW - two-phase flow

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EP - 3453

JO - Nonlinearity

JF - Nonlinearity

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ER -

Weak solutions for a non-Newtonian diffuse interface model with different densities

Abstract

Keywords

ASJC Scopus subject areas

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